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arXiv:2308.13090 · Physical Review A

Interspecies spin-noise correlations in hot atomic vapors

K. Mouloudakis, F. Vouzinas, A. Margaritakis, A. Koutsimpela, G. Mouloudakis, V. Koutrouli, Michalis Skotiniotis, Giorgos P. Tsironis, Michail Loulakis, Morgan W. Mitchell, Georgios Vasilakis, Iannis K. Kominis

Published Nov 27, 2023• 16 citations
arXivHTMLPDF

Abstract

We report an experimental and theoretical study of spin-noise correlations in a $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ unpolarized alkali-metal vapor dominated by spin-exchange collisions. We observe strong unequal-time interspecies correlations and account for these with a first-principles theoretical model. Since the two atomic species have different spin precession frequencies, the dual-species vapor enables the use of an additional experimental handle, the applied magnetic field, for untangling various subtypes of spin correlations. In particular, the measured cross-correlation and autocorrelation spectra shed light on a number of spin-dynamic effects involving intra-atom, interatom, intraspecies, and interspecies correlations. Cross-correlation coefficients exceeding $60%$ have been observed at low magnetic fields, where the two spin species couple strongly via spin-exchange collisions. The understanding of such spontaneously generated correlations can motivate the design of quantum-enhanced measurements with single or multispecies spin-polarized alkali-metal vapors used in quantum sensing applications.

DOI
10.1103/physreva.108.052822

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We report an experimental and theoretical study of spin-noise correlations in a 87Rb\ensuremath-133Cs^{87}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}87Rb\ensuremath-133Cs unpolarized alkali-metal vapor dominated by spin-exchange collisions. We observe strong unequal-time interspecies correlations and account for these with a first-principles theoretical model. Since the two atomic species have different spin precession frequencies, the dual-species vapor enables the use of an additional experimental handle, the applied magnetic field, for untangling various subtypes of spin correlations. In particular, the measured cross-correlation and autocorrelation spectra shed light on a number of spin-dynamic effects involving intra-atom, interatom, intraspecies, and interspecies correlations. Cross-correlation coefficients exceeding 6060%60 have been observed at low magnetic fields, where the two spin species couple strongly via spin-exchange collisions. The understanding of such spontaneously generated correlations can motivate the design of quantum-enhanced measurements with single or multispecies spin-polarized alkali-metal vapors used in quantum sensing applications.
The physics of spin exchange collisions has fueled a large number of discoveries in fundamental physics, chemistry and biology, and has led to several applications in medical imaging and nuclear magnetic resonance. We here report on the experimental observation and theoretical justification of a novel effect, the transfer of spin noise from one atomic species to another, through the mechanism of spin exchange. Essentially, we extend the foundational studies of spin exchange into the deeper layer of quantum fluctuations. The signature of spin noise exchange is an increase of the total spin noise power at low magnetic fields where the two-species spin noise resonances overlap.
We present a first-principles analysis of the noise spectra of alkali-metal vapors in and out of the spin-exchange-relaxation-free (SERF) regime, and we predict nonintuitive features with a potential to further improve the sensitivity of SERF media, and which must be taken into account in their use in quantum optical applications. Studying the process of spin-noise spectroscopy (SNS), we derive analytic formulas for the observable noise spectra, and for the correlation functions among different hyperfine components, which give additional insight into the spin dynamics. The analytic results indicate a variety of distortions of the spin-noise spectrum relative to simpler models, including a broad spectral background that mimics optical shot noise, interference of noise contributions from the two ground-state hyperfine levels, noise reduction at the spin-precession frequency, and ``hiding'' of spin-noise power that can introduce a systematic error in noise-based calibrations, e.g., for spin-squeezing experiments.
For spin-polarized ensembles of alkali-metal atoms with hyperfine structure and spin greater than 1/2, the interplay between spin dynamics and quantum noise mechanisms remains largely unexplored, especially in the spin-exchange-relaxation-free (SERF) regime. In particular, the theoretical understanding of the dynamics for the mean values of the spin operators was established shortly after the advent of optical pumping. In contrast, a corresponding theory for spin fluctuations has not yet been developed, and is addressed in this work. Here, we develop such a first-principles theory of spin fluctuations in alkalimetal vapors. The nonlinearity bottleneck of spin-exchange collisions, which dominate the physics of such vapors, is overcome by linearizing the dynamics around the equilibrium density matrix. The result is a precise calculation of the absolute magnetic sensing limit of optically pumped atomic magnetometers, which can precisely benchmark quantum limited and quantum enhanced protocols, in contrast to the traditional approach shown to be adequate only within a factor of 2. Further, we elucidate how signal and noise in atomic magnetometers are distributed among the spin eigenmodes defined under continuous optical pumping and probing via the paramagnetic Faraday rotation. Notably, in the SERF regime, alongside the magnetic resonance narrowing, we find a reduction of spin noise at the spin-precession frequency as a consequence of strong hyperfine correlations redistributing spin noise, when both hyperfine manifolds are simultaneously probed. These insights can lead to improved quantum devices utilizing alkali-metal atoms or similar spin-based sensing platforms.
Random spin-exchange collisions in warm alkali vapor cause rapid decoherence and act to equilibrate the spin state of the atoms in the vapor. In contrast, here we demonstrate experimentally and theoretically a coherent coupling of one alkali species to another species, mediated by these random collisions. We show that the minor species (potassium) inherits the magnetic properties of the dominant species (rubidium), including its lifetime (T_{1}), coherence time (T_{2}), gyromagnetic ratio, and spin-exchange relaxation-free magnetic-field threshold. We further show that this coupling can be completely controlled by varying the strength of the magnetic field. Finally, we explain these phenomena analytically by mode mixing of the two species via spin-exchange collisions.
Spin-exchange collisions in alkali or alkali-noble gas vapors are at the basis of quantum sensing, nucleon structure studies, tests of fundamental symmetries, and medical imaging. We here show that spin-exchange collisions in hot alkali vapors naturally produce strong bipartite entanglement, which we explicitly quantify using the tools of quantum information science. This entanglement is shown to have a lifetime at least as long as the spin-exchange relaxation time, and to directly affect measurable spin noise observables. This is a formal theoretical demonstration that a hot and dense atomic vapor dominated by random spin-exchange collisions can support long-lived bipartite and possibly higher-order entanglement.